The alternative is laborious, involves expressions, and doesn't always work depending on the scene.

[Moog Gravett]"3) I'd quite like to have a heat haze, but only affecting the rear of the scene. I'm going to try and set up a distortion on a plane and place it in the 3D scene, but the plane would probably need to be really large. Is there a more efficient way? Maybe using an adjustment layer?"

If the layer is going to remain distant from the camera then it does not need to be high resolution. Around the resolution of your composition should be fine. As you move this layer away from the camera you can scale it up and lose no detail in the image.

The best way I can recommend to do this is to use an adjustment layer with Distort > Displacement Map and Blur & Sharpen > Compound Blur. If you pre-compose the 3D "heat haze" displacement source and collapse transformations then you just have to point those effects to that pre-comp.